The motion of a driven Brownian object in a periodic force field has been studied extensively for half a century, not only because of its intrinsic interest, but also because of its close relationship to such disparate physical phenomena as charge transport in Josephson junctions and the kinetics of chemical reactions. Most studies have focused on biased diffusion in one-dimensional systems, the tilted washboard problem providing the archetype for the field. Even this much-studied model continues to yield surprises, with giant enhancement of thermal fluctuations recently having been discovered for particles that are marginally trapped by the washboard.
Higher-dimensional systems have a substantially richer phenomenology because the driven particle enjoys the additional freedom of selecting its course through the force landscape. The force field itself can have a richer variety of characteristics including multidimensional symmetries and solenoidal components that give rise to interesting non-equilibrium effects. Because the particle can move around obstacles, the force landscape can even consist of impenetrable barriers. How a Brownian particle finds its way through such structured terrains remains incompletely understood.